The present application generally relates to dispatching energy, e.g., an electric power. More particularly, the present application relates to determining an amount of electric power to be generated and their cost to generate while meeting at least one contingency constraint and one or more customer requests.
Electricity markets in the United States are comprised of two interconnected markets: a day ahead market and a real-time or balancing market. The day-ahead market focuses on an electricity power generation schedule per an electric power generator. The real-time market focuses on economic dispatch, i.e., determining an output of an electric power generator and its cost to generate the electric power.
Currently, linear direct current (DC) approximation of a (nonlinear, non-convex) AC (Alternating Current) power flow equation is mostly used in the existing electric power generation systems. A reference to P. N. Biskas and A. G. Bakirtzis, entitled “A decentralized solution to the security constrained DC-OPF problem of multi-area power systems,” Power Tech, 2005 IEEE Russia, pp. 1-7, June 2005, wholly incorporated by reference as if set forth herein, describes the linear direct current approximation of the AC power flow equation in detail. A main drawback of the linear DC approximation is that it does not capture a physical electric power flow more realistically than the AC power flow equation. Currently, solving the AC power flow equation without the linear DC approximation requires large amount of memory usage (e.g., more than one Terabyte, etc.) and cannot be performed in real-time. Currently, the solution of the AC optimal power flow problem is usually a low quality, i.e., far from an optimal solution (i.e., optimality referring to ideal amount of electric power to be generated at an ideal cost to generate the ideal amount of electric power). The linear DC approximation requires trials and errors to ensure a feasibility of its solution and does not provide an optimal solution.